This has come up in the older forum discussions. Users mostly discuss the logic, approach and design without sharing their actual scripts. Have you checked what they’ve tried and what problems they’ve run into?
I get what you’re asking for: keep the same profile and device identity while moving to the latest BAS browser version. That would be useful. But changing the version in the User-Agent and related fields may only cover part of it.
A newer browser can introduce new features or change how existing ones behave. The fingerprint/emulation layer may need changes too, otherwise you could end up with a fingerprint that claims one version but behaves differently.
Keeping all of that consistent across updates could be quite a headache. Maybe that’s one reason there’s no built-in feature for this, though that’s just my guess.
Personally, I don’t expect the BAS developers to implement this feature themselves. I think users who need it have little choice but to build and maintain their own solutions and scripts, adapting them as browser versions change.